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1
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Let P be a variable point on the parabola $$y = 4{x^2} + 1$$. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :
A
$${(3x - y)^2} + (x - 3y) + 2 = 0$$
B
$$2{(3x - y)^2} + (x - 3y) + 2 = 0$$
C
$${(3x - y)^2} + 2(x - 3y) + 2 = 0$$
D
$$2{(x - 3y)^2} + (3x - y) + 2 = 0$$
2
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Let the tangent to the parabola S : y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :
A
$${{25} \over 2}$$
B
$${{35} \over 2}$$
C
$${{15} \over 2}$$
D
25
3
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Consider a hyperbola H : x2 $$-$$ 2y2 = 4. Let the tangent at a
point P(4, $${\sqrt 6 }$$) meet the x-axis at Q and latus rectum at R(x1, y1), x1 > 0. If F is a focus of H which is nearer to the point P, then the area of $$\Delta$$QFR is equal to :
A
$${\sqrt 6 }$$ $$-$$ 1
B
$${7 \over {\sqrt 6 }}$$ $$-$$ 2
C
$${4\sqrt 6 }$$ $$-$$ 1
D
$${4\sqrt 6 }$$
4
JEE Main 2021 (Online) 18th March Evening Shift
Let a tangent be drawn to the ellipse $${{{x^2}} \over {27}} + {y^2} = 1$$ at $$(3\sqrt 3 \cos \theta ,\sin \theta )$$ where $$0 \in \left( {0,{\pi \over 2}} \right)$$. Then the value of $$\theta$$ such that the sum of intercepts on axes made by this tangent is minimum is equal to :
$${{\pi \over 6}}$$
$${{\pi \over 3}}$$
$${{\pi \over 8}}$$
$${{\pi \over 4}}$$